The measurement of the optical transfer function, OTF, of an optical system with sampled images may suffer from aliasing effects. Reducing the impact of these aliasing effects improves measurement accuracy. Previous work has been done by applying the two dimensional Fourier transform using a tilted one dimensional pattern. See applicant's U.S. Pat. No. 5,621,519, issued Apr. 15, 1997 to Frost et al., entitled "Imaging system Transfer function Control Method and Apparatus", which is incorporated herein by reference.
The output signal of a charge coupled device, CCD, sensor, is the spatially sampled version of the input signal to the CCD. The frequency representation of the spatially sampled version of the input signal suffers from an aliasing effect. This alias effect degrades the estimation of frequency measurements, especially, below and near the Nyquist frequency. In addition, the frequency components above the Nyquist frequency cannot be estimated.
In Frost et al. the rotated one dimensional pattern in small degree is employed. The two dimensional Fourier transform of the rotated one dimensional pattern lies in the line which is rotated through the same angle and passes through the origin. For this reason, in Frost et al. the frequency components over the Nyquist frequencies may be separated and the alias effects may be removed. However, this method needs a two dimensional Fast Fourier Transform, FFT, or equivalent. In many real-time implementations, an optimization process is needed to estimate the two dimensional FFT accurately. The two dimensional FFT may take an unacceptably long time and may suffer a loss in accuracy. The one dimensional FFT is faster than the two dimensional FFT and can be estimated with high precision in real time.
The OTF is a quantitative measure of the quality of an imaging system. In an imaging system that is to be used for automated image processing and analysis it is important to have a quantitative measure of the quality of the imaging system. This quantitative measure allows appropriate interpretation of other quantitative measures that are obtained using the imaging system. For example measurements taken with the optical system of the texture of objects, or optical density of objects will be affected by the optical system where the OTF is a measure of that effect. Thus the same objects imaged by two different optical systems may result in differing measurements. Also an unacceptably poor OTF may indicate a failure of the optical system to deliver adequate images suitable for further analysis.